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Chapter 4: Problem 23

Assume the variables \(a=2, b=4,\) and \(c=6 .\) Circle the \(T\) or \(F\) for each of the following conditions to indicate whether its value is true or false.

Short Answer

Expert verified
Question: Determine if each of the following conditions is True (T) or False (F) given the values of a, b, and c as 2, 4, and 6 respectively. 1. \(a < b\) 2. \(b > c\) 3. \(a + b = c\) 4. \(b - a = c\) 5. \(ac = 2b\) Answer: 1. True (T) 2. False (F) 3. True (T) 4. False (F) 5. False (F)

Step by step solution

01

Condition 1: \(a < b\)

We are given \(a=2\) and \(b=4\). Comparing the two, we observe that \(2 < 4\). Therefore, this condition is True (T).
02

Condition 2: \(b > c\)

We are given \(b=4\) and \(c=6\). Comparing the two, we observe that \(4\) is not greater than \(6\). Therefore, this condition is False (F).
03

Condition 3: \(a + b = c\)

We are given \(a=2, b=4,\) and \(c=6\). Checking if \(a + b = c\), we calculate \(2 + 4 = 6\). Since both sides are equal, this condition is True (T).
04

Condition 4: \(b - a = c\)

We are given \(a=2, b=4,\) and \(c=6\). Checking if \(b - a = c\), we calculate \(4 - 2 = 2\). Since these values are not equal, this condition is False (F).
05

Condition 5: \(ac = 2b\)

We are given \(a=2, b=4,\) and \(c=6\). Checking if \(ac = 2b\), we calculate \(2 \times 6 = 12\) and \(2 \times 4 = 8\). Since these values are not equal, this condition is False (F). To summarize the results: 1. \(a < b\) is True (T) 2. \(b > c\) is False (F) 3. \(a + b = c\) is True (T) 4. \(b - a = c\) is False (F) 5. \(ac = 2b\) is False (F)

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Most popular questions from this chapter

The following truth table shows various combinations of the values true and false connected by a logical operator. Complete the table by circling T or \(\mathrm{F}\) to indicate whether the result of such a combination is true or false. $$\begin{array}{lcc} \text { Logical Expression } & \text { Result (circle T or F) } \\ \text { True AND False } & \mathrm{T} & \mathrm{F} \\ \text { True AND True } & \mathrm{T} & \mathrm{F} \\ \text { False AND True } & \mathrm{T} & \mathrm{F} \\ \text { False AND False } & \mathrm{T} & \mathrm{F} \\ \text { True OR False } & \mathrm{T} & \mathrm{F} \\ \text { True or True } & \mathrm{T} & \mathrm{F} \\ \text { False or True } & \mathrm{T} & \mathrm{F} \\ \text { False or False } & \mathrm{T} & \mathrm{F} \\ \text { Not True } & \mathrm{T} & \mathrm{F} \\ \text { NOT False } & \mathrm{T} & \mathrm{F} \end{array}$$

If the following pseudocode were an actual program, what would it display? Declare String s1 = "New York" Declare String s2 = "Boston" If s1 > s2 Then Display s2 Display s1 Else Display s1 Display s2 End If

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